Asymmetric high speed Digital Subscriber Line (ADSL) and Very high speed Digital Subscriber Line (VDSL) are examples of modem communication systems which permit transmission of data over band-limited communication lines at very high rates, e.g., up to 52 Mbits/s. They are examples of multi-carrier systems. Reference is made to “ADSL, VDSL and Multicarrier Modulation”, J. A. C. Bingham, Wiley, 2000. Multi-carrier modulation is a well known means of transmitting digital data by splitting that data into fixed-length data “blocks” o “symbols” each having the same number of sub-blocks or bits. Analog transmission of these blocks is carried out using a set of carrier signals. There is a carrier for each of the sub-blocks in one block. The carriers have frequencies which are equally spaced across the transmission band of the transceiver. One such arrangement is called DMT (Discrete multi-tone). DMT modems transmit data by dividing it into several interleaved bit streams, and using these bit streams to modulate several carriers. Another application of multicarrier modulation is in OFDM systems, as described for instance in “ODFM for Wireless Multimedia Communications”, R. van Nee and R. Prasad, Artech House, 2000. Applications are for example, wireless LAN's. This modulation technique also finds application in Satellite communications, see for example, “Satellite Communications Systems”, G. Maral, M. Bousquet, Wiley, 1998.
A significant limitation in a multiple carrier system is intersymbol interference (ISI) and/or intercarrier interference (ICI). ISI is essentially caused by delays in the transmission path which can vary with frequency. Since a typical signal pulse can be regarded as having components at many frequencies, the effect of a dispersive channel is to spread or “disperse” the pulse in the time domain, and cause overlap with neighboring pulses. The average duration of the delays and the variation or range of the delays, varying with time and frequency for example, cause wave “dispersion” and overlap into neighboring pixels and hence ISI. Small amounts of ISI can cause a disproportional amount of distortion in the output of the demodulator used to recover the original data signals. The original data symbols can be recovered accurately provided the transfer function of the dispersive channel can be found/simulated.
One way to compensate for ISI in a DMT system is to add a cyclic prefix (CP) (guard time) to the beginning of each transmitted DMT symbol. This CP absorbs the overlap caused by dispersion and can be discarded. Unfortunately, while increasing the length of prefixes reduces ISI, it also decreases the effective data rate. Another approach, which can be used in conjunction with the CP technique or not, is to employ an equalizer at the receiver. However many equalizers require considerable and ongoing computation “overhead.”
Equalization involves correcting or compensating for the effect of the dispersive channel on the received signal. Generally, the frequency response of the channel is not known accurately, nor is the time domain response. Accordingly, an equalizer is designed using numerous parameters that must be adjusted on the basis of measurements of a channel's signal-affecting characteristics. It is known to have nested equalizers for equalizing separately in the time domain and the frequency domain. One known technique is a time domain equalizer (TDEQ) employed to shorten the effective delay from the dispersive channel. It is generally a linear digital filter arranged to shrink the total impulse response of the channel to the length of CP+1 symbol, such that the overlap from one symbol lands in the CP but does not interfere with the next symbol. In a DMT receiver, following TEQ, the CP is removed, followed by a Fast Fourier Transform (FFT), complementary to the IFFT of the transmitter. The signal can be then passed to a frequency domain equalizer (FDEQ), to recover the transmitted symbols, e.g. QAM symbols from which the bit streams are recovered.
A transversal filter is a common choice for a linear equalizer. The tap coefficients correspond to the channel parameters and represent a “model” of the dispersive nature of the channel. If the coefficients are properly selected, the equalizer can attenuate ISI significantly.
Equalization can involve a training sequence that is compared at the receiver with a locally-generated or otherwise known training sequence (cross-correlation). Adaptive equalization involves adapting the coefficients continually and automatically directly from the received data. A drawback of adaptive equalization is the computational “cost” involved in continually updating the filter coefficients so that the channel model is adapted to the current conditions of the channel.
U.S. Pat. No. 6,408,022 (Fertner) shows reducing both computational cost and cyclic prefix extension, but at the same time effectively equalizing received signals to compensate for ISI using a short length equalizer. Krakovian calculus is used to determine optimum time-domain equalizer coefficients using a selected offset and an established cost function. The implementation involves taking advantage of the Toeplitz structure of a krakovian structure.
U.S. Pat. No. 6,404,806 (to Ginesi, et al.) shows an example of an ADSL system having a TDEQ including an estimation of, and compensation for, echo on the line and the ingress of out of band noise, particularly RFI, into the in band channels. To reduce both the complexity of the TDEQ and duplexing filters, a method for training the TDEQ is used, which includes computing a Toeplitz autocorrelation matrix.
U.S. Pat. No. 6,353,629 (to Pal) shows time domain equalization techniques referred to as poly-path time domain equalization techniques; improved training methods for training transmitters and/or receivers of a data transmission system; and
techniques for providing time domain equalization to a transmitter side of a data transmission system. The training methods involve Toeplitz matrices.
U.S. Pat. No. 6,233,276 (to Simeon) shows using a time domain filter or equaliser, with a reduced number of digital filter coefficients. The full-length equalizer channel impulse response is truncated by first selecting a subset of contiguous filter samples followed by windowing and convolution with a time domain representation of a frequency domain filter. The result is a shorter equalizer having fewer coefficients so as to improve data transmission rate.
U.S. patent application 20020106035 A1 (Harikumar, Gopal et al.) shows a spectrally constrained impulse shortening filter for time domain equalisation in a DMT receiver. A target spectral response is calculated and the impulse response of the channel shortened so that a significant part of an energy of the impulse response is confined to a region that is shorter than a target length.